Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Uniformly high order accurate essentially non-oscillatory schemes, III
Journal of Computational Physics
Reconstructing volume tracking
Journal of Computational Physics
Journal of Computational Physics
Second-order phase field asymptotics for unequal conductivities
SIAM Journal on Applied Mathematics
Modeling melt convection in phase-field simulations of solidification
Journal of Computational Physics
Journal of Computational Physics
Nonlinear preconditioning for diffuse interfaces
Journal of Computational Physics
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Computation of multiphase systems with phase field models
Journal of Computational Physics
A volume of fluid method based on multidimensional advection and spline interface reconstruction
Journal of Computational Physics
Second-order accurate volume-of-fluid algorithms for tracking material interfaces
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Sharp interface Cartesian grid method III: Solidification of pure materials and binary solutions
Journal of Computational Physics
A conservative level set method for two phase flow
Journal of Computational Physics
Journal of Computational Physics
A fast and accurate semi-Lagrangian particle level set method
Computers and Structures
Shape and topology optimization based on the phase field method and sensitivity analysis
Journal of Computational Physics
A conservative phase field method for solving incompressible two-phase flows
Journal of Computational Physics
Anti-diffusion method for interface steepening in two-phase incompressible flow
Journal of Computational Physics
Numerical and computational efficiency of solvers for two-phase problems
Computers & Mathematics with Applications
Segmentation of Stochastic Images using Level Set Propagation with Uncertain Speed
Journal of Mathematical Imaging and Vision
Hi-index | 31.46 |
A general interface tracking method based on the phase-field equation is presented. The zero phase-field contour is used to implicitly track the sharp interface on a fixed grid. The phase-field propagation equation is derived from an interface advection equation by expressing the interface normal and curvature in terms of a hyperbolic tangent phase-field profile across the interface. In addition to normal interface motion driven by a given interface speed or by interface curvature, interface advection by an arbitrary external velocity field is also considered. In the absence of curvature-driven interface motion, a previously developed counter term is used in the phase-field equation to cancel out such motion. Various modifications of the phase-field equation, including nonlinear preconditioning, are also investigated. The accuracy of the present method is demonstrated in several numerical examples for a variety of interface motions and shapes that include singularities, such as sharp corners and topology changes. Good convergence with respect to the grid spacing is obtained. Mass conservation is achieved without the use of separate re-initialization schemes or Lagrangian marker particles. Similarities with and differences to other interface tracking approaches are emphasized.